外文翻译--激光切割陶瓷砖的速度：理论和经验值的比较

1、徐州工程学院毕业设计外文翻译学生姓名学院名称机电工程学院专业名称机械设计制造及其自动化指导教师 原文：laser cutting speeds for ceramic tile: a theoretical-empirical comparisoni. black *department of mechanical and chemical engineering, heriot-watt university, riccarton, edinburgh eh14 4as, ukreceived 21 october 1997; accepted 24 march 1998abstractth

2、is paper presents a comparison of theoretically-predicted optimum cutting speeds for decorative ceramic tile with experimentally-derived data. four well-established theoretical analyses are considered and applied to the laser cutting of ceramic tile, i.e. rosenthals moving point heat-source model an

3、d the heat balance approaches of powell, steen and chryssolouris. the theoretical results are subsequently compared and contrasted with actual cutting data taken from an existing laser machining database. empirical models developed by the author are described which have been successfully used to pre

4、dict cutting speeds for various thicknesses of ceramic tile. # 1998 elsevier science ltd. all rights reserved.keywords: co laser ceramic materials advanced cutting processes laser modeling cutting speeds1. list of symbolsa absorptivitya thermal di.usivity (m2/s)c specific heat (j/kg k)d cutting dept

5、h (mm)e specific cutting energy (j/kg)k thermal conductivity (w/m k)j laser beam intensity (w/m2)l latent heat of vaporisation (j/kg)l length of cut (mm)n coordinate normal to cutting frontp laser power (w)p laser power not interacting with the cutting front (w)q heat input (j/s)r radial distance (m

6、m)r beam radius (mm)s substrate thickness (mm)s critical substrate thickness (mm)t temperature ()t ambient temperature ()t peak temperature ()t temperature at top surface ()t time (s)v cutting speed (mm/min)v optimum cutting speed (mm/min)w kerf width (mm)x, y, z coordinate locationx, y, z coordinat

7、e distance (mm) conductive loss function radiative loss function convective loss function angle between z-coordinate and x-coordinate (rad)n coordinate parallel to bottom surface angle of inclination of control surface w.r.t. x-axis (rad)v coupling coecient translated coordinate distance (mm) densit

8、y (kg/m) angle of inclination of control surface w.r.t. y-axis (rad)2. introductionlaser cutting of a decorative ceramic tile has its own set of characteristic problems including burnout,striations, dross and out-of-flatness, which all affect the finish quality of a cut edge 1-3. a typical cut may h

9、ave some or all of these features depending on the type of ceramic tile being processed and on the setting of the various set-up parameters. in a production environment, cutting speeds need to be optimised in order to reduce in-cut times without too much significant degradation of cut-edge quality.

10、an optimum cutting speed can be defined as that which will produce full-through-cutting (ftc) with minimal micro-cracking both in the surface glaze and in the tile substrate.therefore, it can be argued that the cutting speed necessary to raise approximately a cuboid of material of dimensions l, w an

11、d s to the materials melting or fusion temperature would be equal to the cutting speed that will just cut the material; higher cutting speeds will not allow ftc and on the other hand slower cutting speeds will result in the material absorbing more heat and reaching higher temperatures than is necess

12、ary to cut the tile. these higher temperatures will also result in greater thermal gradients and residual stresses, with the subsequent problems of micro-cracking in the surface glaze together with excess dross. striation marks will also be exaggerated at slower cutting speeds and this will also red

13、uce cut finish quality. it should also be noted that the various theoretical approaches outlined in this paper relate only to laser cutting in continuous wave (cw) mode.3.theoretical approaches3.1. calculating v using moving point heat-source analysis at its simplest level, laser cutting can be cons

14、idered to be a moving point heat-source problem where the point heat source is assumed to be the laser beam focused on the material to be cut moving at a constant cutting speed. therefore, it is not unreasonable to utilise the heat-flow solutions determined by rosenthal and as applied by easterling

15、4. in this analysis it is assumed that the energy of the cutting source moves with constant speed along the x-axis of a fixed rectangular co-ordinate system as shown in fig. 1. ignoring radiative and convective heat transfer effects, the differential equation of heat flow expressed in the co-ordinat

16、es shown in fig. 1 is given by eq. (1).however, this equation essentially refers to a fixed coordinate system and may be modified to a moving coordinate system by replacing x with , where is the distance of the point heat source from some fixed position along the x-axis, which is dependent on the sp

17、eed of the moving source as defined by = x - v.when differentiated with respect to , eq. (1) yieldsand this equation can be simplified by assuming that a quasistationary temperature distribution exists. this means that the temperature distribution around a heat source of uniform velocity will settle

18、 down to a constant form, i.e. t/t= 0 provided q/v is constant. this is not an unreasonable assumption for the laser cutting of ceramic tile. therefore eq. (1) can be simplified to givethis differential equation can now be solved for both thick and thin ceramic tile substrates, since in effect, the

19、flow of heat is approximately two-dimensional for thin tiles and three-dimensional for thick ones. in the case of thin tiles, the heat transfer will be primarily by conduction, other effects being negligible. eq. (4) gives the temperature-time distribution for three-dimensional heat flow (thick tile

20、s) and eq. (5) is the solution for two-dimensional heat flow (thin tiles), where the choice of either 2d or 3d heat flow is not only governed by tile thickness but also by material type. a critical thickness which defines the crossover, or boundary condition between the two can be derived by equatin

21、g the thick and thin plate approaches and is given bythe relationship between s and v can be plotted graphically for the given laser cutting conditions, i.e. q3450 w (the maximum rated power of the laser cutter used), c800 j/kg k, r3380 kg/m3 (representative values for ceramic tile) and t=18 (ambien

22、t temperature) (fig. 2).fig. 2 is useful because if the range of cutting speeds for a given thickness of tile falls below the curve shown then the tile should be treated as a 2d (thin tile) case. however if a range of cutting speeds for a given tile lies in the regime above the curve then the 3d (th

23、ick tile) approach should be applied. it should be noted that for a tile whose range of cutting speeds straddles the curve on either side the thin tile case should only be considered.it is possible, by simplifying eqs. (4) and (5), to eliminate the time variable to obtain eq. (7) for the thick tile

24、case and eq. (8) for a thin tile case wherein the thin case, the distance in the direction of the z-axis can be ignored. also by letting r= y, the temperature profile can be examined in the direction of the y-axis. the following graphs were constructed using eq. (8); eq. (7) was not used as the tile

25、s to be investigated straddled a range of cutting speeds. it should be noted that the cut zone referred to in fig. 3 extends to an area corresponding to r = 0.5 mm (i.e. the beam radius).the curves in fig. 3 show that by increasing v the peak temperature within the cut zone is reduced. they also sho

26、w the optimum cutting speed that will cut the tiles, which occurs at the intersection with the line representing the representative melt temperature of ceramic tile, i.e. t=1327 (1600 k). any cutting speed above this line should, in theory, produce ftc and any that fall below will not cut the tile.

27、note that thermal conductivity plays no part in eqs. (7) and (8).in the calculation of v, eqs. (7) and (8) are applied depending on whether the tile was considered to be thick or thin as defined by eq. (6). to calculate v for a thin case, e.g. 3.7 mm, eq. (8) can be arranged to giveletting q= p. the

28、 distance in the direction of the z-axis is omitted from the expression for radial distance because the substrate thickness takes this parameter into consideration; therefore r = r. however, in the case of the thicker tile eq. (7) can be arranged to givewhere r = (0.510)+ s. for both cases the peak

29、temperature is set to equal the melt temperature of the tile.3.2. calculating v using heat balance modelspowell 5 presents an analysis in which, during laser cutting, a dynamic equilibrium exists in the cut zone that balances the incoming energy and material with the outgoing energy and material. th

30、erefore a simple energy balance for laser cutting can be expressed as energy supplied to cut zone= energy used in generating a cut + energy losses from the cut zone(by conduction, radiation, etc.)this can be expressed as the following formulaif it is assumed that all of the laser power transmitted t

31、hrough the cut zone interacts with the cut front (p=0), that all laser power is absorbed by the tile substrate (a = 1) and that the conductive, radiative and convective losses are negligible, then the above equation reduces to where w= 2r. since the cut zone for good quality cw cuts rarely exceeds a

32、 few microns the previous assumptions are not unreasonable. noting that for full through cutting, v =l/t, rearranging the above formula gives similarly, steen 6 presents an analysis in which the cutting process can be approximately modelled by assuming all the energy enters the cut zone and is remov

33、ed before significant conduction occurs (i.e. no significant energy loss). the outcome is a simple equation based on the heat balance for the material removed.if we assume that n31 when v = v, then eq. (14) reduces towhich is the same as eq. (13). this is to be expected since both powell and steen u

34、se basically the same energy balance approach.as an enhancement of the above, chryssolouris presents a general model 7 based principally on a heat balance at the erosion front and a temperature calculation inside a material from heat conduction equations. in order to give a quantitative understandin

35、g of the effect of the different process parameters on the cutting process, an infinitesimal control surface on the erosion front surface is shown in fig. 4.the control surface is inclined at an angle y with respect to the x-axis and at an angle with respect to the y-axis, and is subjected to a lase

36、r beam of intensity j(x, y). the cartesian co-ordinate system (x, y, z) is moving with the laser beam which has intensity profile j(x, y) projected onto the control surface. the heat balance at the control surface isin order to derive simple analytical relations, simplifications need to be made. for

37、 instance, although heat is conducted three-dimensionally near the erosion front due to the presence of a bottom surface in cutting, which behaves as an adiabatic boundary, the heat conduction occurs two-dimensionally (downward conduction is negligible compared with conduction in other directions).

38、thus, in cutting it is assumed that heat is conducted two-dimensionally into the solid, so that the conduction term in eq. (16) can be simplified aswhich gives the heat balance condition at the cutting front. the temperature gradient at the erosion front, assuming that the conduction area and direct

39、ion do not change, can be determined by solving the following 1d heat conduction equationfrom eq. (18) the temperature distribution inside the solid can be determined and differentiation of this gives the following temperature gradient at the erosion frontby substituting the temperature gradient int

40、o the heat balance, an equation for the erosion front slope (i.e. tan ) in the cutting direction can be obtained. this slope is said to have an infinitesimal depth which forms an integral which, upon integration, gives an expression for the depth of cutby setting d= s and the melt temperature at the

41、 top surface along the centre line of the cut, t1327, a value of v can be calculated for a specific type and thickness of tile, where (again) p450 w, r3380 kg/m, d = 2r = 1.010m，l856.410 j/kg ，c 800 j/kg k ，t =18and a = 1. therefore, eq. (20) can be arranged to givewhich, again, is similar to the fo

42、rmula derived from steen and powells analysis.4. comparison with empirical modelsan empirically-derived laser machining database for cutting ceramic tile has been compiled from extensive (and ongoing) experimental work in the department of mechanical and chemical engineering at heriot-watt universit

43、y. the database contains specific information on cutting speeds associated with variation in such cutting parameters as shield gas type and pressure, nozzle size, focal point and, most importantly, surface finish quality. table 1 below gives a comparison between v from this database with the previou

44、sly described theoretical approaches. note that, where available, a range of values is given from the database since ceramic tile is a non-homogeneous material and cutting conditions will vary markedly from one tile to another.mean values of v were used to establish a best fit curve for the cutting

45、data according to a method initially devised by thomson 3, in which the empirical curve is plotted for the rated power of the laser cutter used and fitted to the following formulaewhere a, b, c and d are constants.this can be done in a variety of ways. the normal method to use is to take four points

46、 from the plotted graph and solve these simultaneously. the formula generated by fitting these coefficients back into eq. (1) should then be checked to ensure that it follows the experimental curve and does not deviate beyond the upper and lower limits. if the first set of coefficients proves unsati

47、sfactory, the process is repeated but different start points are chosen, or one or more of the coefficients a, c or d is set to zero. cutting speeds at the machine limit should not be used when generating formulae for the curves, since the governing factor at these limits is no longer the process. f

48、or the given set of data for decorative ceramic tile, the following empirical equation was determinedwith c = d= 0.livingstone and black 1 developed an empirical equation describing the behaviour of v with s for the ftc of decorative ceramic tile which followed an exponential relationship of the for

49、mwhere and are constants determined by the least-squares method. for the data presented in table 1, an equation of the formresulted. the theoretical results predicted in table 1 are represented graphically in fig. 5, together with the empirical curves derived from the database results.5. concluding

50、remarksfig. 5 shows that the predictive models describe a decrease in vopt with an increase in tile thickness, v 1/s. this is what would be expected in practice. the differences between the individual theoretical predictions of v can be ascribed to the different analytical approaches taken in formul

51、ating a suitable cutting model. however, probably the most significant factor in the difference between predicted and experimental values of v is the variation in thermal and material properties between and throughout the different makes of ceramic tile. for instance, spanish makes of tile are consi

52、derably denser and also able to retain more heat during cutting than the other types of tile considered 2.in addition to the vagaries of ceramic tile composition, the theoretical models utilised incorporate some or all of the following assumptions(1) a moving point source represents the laser beam.(

53、2) the specific heat capacity is unaffected by changes in tile temperature or changes in state.(3) the latent heat of fusion due to phase transformations is neglected.(4) effects of the shield gas are neglected.(5) all the heat input of the laser beam is absorbed in cutting.(6) the kerf is assumed t

54、o have simple 2d geometry with no slope on the cutting front (although chryssolouris analysis does take this into account).(7) all of the laser power transmitted through the cut zone interacts with the cutting front.(8) there are negligible conductive, radiative and convective losses during cutting.

55、(9) powells analysis assumes that the cut zone has a high absorptivity due to its high temperature, the presence of absorptive oxides, the shallow angle of incidence to laser beam, its roughness and its absorptive layer of vapour.(10) powells model assumes that the specific energy of cutting is take

56、n to be constant.(11) rosenthals model assumes a quasi-stationary temperature distribution.additionally, the theoretical models presented also take no account of the finish or production method of the final cut. in practice, there may need to be as many as six v/s curves to account for every combina

57、tion of cutting speed and cut quality for each of the following types of machine control:(i) adaptive control, where problems associated with low v can be ignored because the adaptive control can compensate for this.(ii) programmable control, where a curve should be produced for cutting intricate features, since this control system allows switching v and pulsing to compensate.(i